Chapter Review 05 - Time Value of Money Investments and loans base their interest calculations on one of two possible methods: the simple interest and the compound interest methods. Both methods apply three variables-the amount of principal, the interest rate, and the investment or deposit period-to the amount deposited or invested in order to compute the amount of interest. However, the two methods differ in their relationship between the variables. Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using: Compound interest? Simple interest? PV(PV x I x N) O FV PV (PV x I x N) FV PV (PV x I x N) FV PV (1 x I x N) FV FV PV x (1 + I)N O FV PV (1 + I)N Identify whether the following statements about the simple and compound interest methods are true or false. False Statement True All other factors being equal, both the simple interest and the compound interest methods will accrue the same amount of earned interest by the end of the first year. After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest. The process of earning compound interest allows a depositor or investor to earn interest on any interest earned in prior periods. Nicholai is willing to invest $35,000 for eight years, and is an economically rational investor. He has identified three investment alternatives (X, Y, and z) that vary in their method of calculating interest and in the annual interest rate offered. Since he can only make one investment during the eight-year investment period, complete the following table and indicate whether Nicholai should invest in each of the investments. Note: When calculating each investment's future value, assume that all interest is earned annually. The final value should be rounded to the nearest whole dollar. Make this investment? Investment Interest Rate and Method Expected Future Value Yes No 11% compound interest $80,659 X 13% compound interest $93,046 Y $71,400 13% simple interest 7